I'm not sure there's any groundcover that's economic and that won't attract the deer. As another said, though: better they eat the groundcover than the hops?
You'll want perennials that aren't too vigorous; while you want them to out compete the weeds, you don't want them to out compete the hops either. You'll want to be able to mow them without killing them, and not have to pay seeds and planting every year. Buckwheat's not really a good option, in my opinion.
The local coop would probably have species to suggest for you. A legume and grass mix is usually better than a monocrop cover. The best species will vary depending on your area. White clover is regularly used, but personally, in my region, I'd opt for birdsfoot trefoil instead. But that legume grows particularly well in my area, it might not in yours.
As a beekeeper in western Québec, a groundcover mix I'd favor would be made up of birdfoot trefoil, chicory, and meadow foxtail, plus probably some more expensive seeds I'd use sparsely in the hope they'd gradually reseed themselves and multiply (ex: chives). I'm planning on testing it out soon, but I haven't had the chance to do so yet, so I'm mostly basing myself off limited trials, observations, and, mostly, literature.
If there are any orchards in your area, might be worth looking at what seed mixes they are using themselves and going with that.
